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Question
Determine the arithmetic progression whose 3rd term is 5 and 7th term is 9.
Solution
For an A.P.
t3 = 5
`=>` a + 2d = 5 ...(i)
And t7 = 9
`=>` a + 6d = 9 ...(ii)
Subtracting (i) from (ii), we get
4d = 4
`=>` d = 1
Substituting d = 1 in (i), we get
a + 2 × 1 = 5
`=>` a = 3
Thus, the required A.P. = a, a + d, a + 2d, a + 3d, .....
= 3, 4, 5, 6, .....
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